\(A=\left(x-1\right)^2+7\ge7.Với\forall x\in Z\)
Dấu "=" xảy ra khi :
\(\left(x-1\right)^2=0\Leftrightarrow x-1=0\Leftrightarrow x=1\)
Vậy Min A = 7 <=> x = 1
\(B=\left|x-5\right|-3\ge-3\)
Dấu "=" xảy ra khi :
\(\left|x-5\right|=0\Leftrightarrow x=5\)
Vậy Min B = -3 <=> x = 5
\(C=x^2+2x+4\)
\(\Rightarrow C=x^2+x+x+1+3\)
\(\Rightarrow C=x\left(x+1\right)+\left(x+1\right)+3\)
\(\Rightarrow C=\left(x+1\right)^2+3\ge3\)
Dấu "=" xảy ra khi :
\(\left(x+1\right)^2=0\Leftrightarrow x=1\)
Vậy Min C = 3 <=> x = 1
\(D=\left|x-3\right|+\left|x-7\right|\)
\(\Rightarrow D\ge\left|x-3+7-x\right|=4\)
Dấu "=" xảy ra khi :
\(\Rightarrow\left\{{}\begin{matrix}x\ge3\\x\le7\end{matrix}\right.\)
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